This paper proposes a control strategy to address the issue of crystal parallelism errors that affect the performance of the new multi-channel double-crystal monochromator （DCM） system. The control strategy integrates iterative learning control （ILC） and model predictive control （MPC） to reduce random position errors of the slave motor and eliminate repetitive mechanical installation errors， respectively. The parallelism errors between the master and slave crystals are converted into the repetitive reference motion trajectory of the slave motor， and the MPC is used to improve the slave motor position tracking within a single rotation cycle. Meanwhile， ILC iterations are applied during rotation cycles to eliminate repetitive mechanical installation errors. The proposed control strategy is verified using a single-axis motor motion experimental platform. Experimental results demonstrate that the motor position tracking error reaches 1.44″–reduction by 99.64%， 98.52%， 98.26%， and 73.33% as compared to the errors of PID， MPC， DOB+MPC， and ILC+PID combination controller strategies， respectively. The proposed control strategy effectively compensates for crystal parallelism errors and improves parallel alignment accuracy， providing practical application value for the performance enhancement of the new multi-channel DCM system.